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I have been going over Norman Wildberger's Youtube series on 'Algebraic Calculus', and at least for me, his entire thesis is quite interesting; trying to take the infinite out of Calculus.

In his youtube series he surely accomplishes a lot, and demonstrates some fundamental results in elementary Calculus from a purely algebraic approach...my question however is about the flip side. Is there any result that his formulation is $\textbf{not}$ able to obtain?

This is hard for me to demonstrate to myself since there are no "Axioms of Calculus" that he could obtain and be done with it, so is such a question even answerable?

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    $\begingroup$ I think this is an interesting question, and disagree with the downvote. That said, it's important to note that Wildberger's polemics (as distinct from his mathematics) are generally disagreed with, to put it mildly, and I would take them with a large pile of salt. $\endgroup$ Jan 26, 2021 at 23:48
  • $\begingroup$ Yes, haha; I find both intriguing in their own right, but in this series he stayed away from sweeping claims that have earned him infamy and just did maths - I also don't get the downvote but oh well $\endgroup$ Jan 26, 2021 at 23:53
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    $\begingroup$ I don’t suppose that any of his approach is available online in written form? There’s no way in hell that I’m going to watch the YouTube videos — I’d be unlikely to do so even for a topic of much greater interest to me. $\endgroup$ Jan 27, 2021 at 0:02
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    $\begingroup$ Hard agree with Brian M. Scott. I've never seen a mathematician "market" themselves like Wildberger, which got me curious enough to watch his "Problems with Calculus" video (at max speed, anyway). The content was perfectly fine and standard, aside from a vague and unjustified swipe at modern formulations of calculus somehow not having "overcome these difficulties". I don't have even close to enough interest to give similar videos any more of my time, though. It's obviously not produced to interest professional mathematicians. $\endgroup$ Jan 27, 2021 at 6:36
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    $\begingroup$ I agree with @NoahSchweber that the question is interesting, but being interesting is not, in and of itself, sufficient for this site. The actual question seems both tremendously broad (survey all of calculus, and determine where this approach fails), as well as rather opinion-based (whether or not a thing breaks down is a subject of debate). $\endgroup$
    – Xander Henderson
    Jan 27, 2021 at 18:06

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